The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The structure of the lessons includes several opportunities that address conceptual understanding.

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where conceptual understanding for the Topic is outlined.
• Lessons are introduced with a video, “Visual Learning Animation Plus,” at PearsonRealize.com to build conceptual understanding.
• Links within the digital program to outside resources, such as Virtual Nerd, include videos for students that introduce concepts.
• In the Student Practice problems, Do You Understand? reviews conceptual understanding.

The instructional materials do provide students opportunities to demonstrate conceptual understanding independently throughout the grade. For example:

• Lesson 6-2, Do You Understand?, “What do you notice about the corresponding coordinates of the pre-image and image after a reflection across the x-axis?” (8.G.1.1a, b, c and 8.G.1.3)
• Lesson 3-2, Do You Understand? Question 2, “How can you use a graph to determine that a relationship is NOT a function?” (8.F.1.1)
• Lesson 3-3, Practice and Problem Solving Question 11, “Justin opens a savings account with $4. He saves $2 each week. Does a linear function or a nonlinear function represent this situation? Explain.” (8.F.1.2 and 8.F.1.3)
• Lesson 6-1, Do You Understand? Question 2, “Triangle L’M’N’ is the image of triangle LMN after a translation. How are the side lengths and angle measures of the triangles related? Explain.” (8.G.1.1a,b,c, and 8.G.1.3)

Physical manipulatives are not a part of the materials. When manipulatives are to be used by teacher and students, they are referenced in digital format.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The structure of the lessons includes several opportunities to develop these skills.

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where procedural skills for the content is outlined.
• In the Student Practice problems, Do You Know How? is the second section, which provides students with a variety of problem types to practice procedural skills.
• There is additional practice of procedural skills online.

The instructional materials develop procedural skill and fluency throughout the grade level. The instructional materials provide opportunities for students to  demonstrate procedural skill and fluency independently throughout the grade.

• In Lesson 2-3, students solve multi-step equations using the distributive property. (8.EE.3.7b) For example, Do You Know How? Question 5: “Solve the equation -3(x-1) + 7x = 27.” Practice and Problem Solving Question 12, “What is the solution of the equation 3(x + 2) = 2(x + 5)?”
• In Lesson 5-4, students solve systems of equations using elimination. (8.EE.3.8b) For example, Practice and Problem Solving, Question 8: “Solve the system of equations using elimination: 2y - 5x = -2; 3y + 2x = 35.”
• Lesson 6-4, students describe a sequence of transformations involving floor plans using a coordinate plane. (8.G.1.3) For example, Try It!: “Ava decided to move the cabinet to the opposite wall. What sequence of transformations moves the cabinet to its new position?”

In addition, each cumulative assessment spirals through all previous topics, reviewing key information with a a variety of problems to reinforce skills.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The structure of the lessons includes several opportunities for students to engage in application.

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where applications of the content are outlined.
• In the Student Practice problems, Practice & Problem Solving provides students with a variety of problem types to apply what they have learned.
• Each Topic includes a Performance Task, where students apply math of the Topic in multi-step, real-world situations.
• Every Topic also includes a 3-Act Mathematical Modeling application problem.
• Each Topic includes a STEM project which is application; this incorporates more science or engineering.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level as well as provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. Non-routine problems are typically found in Performance Tasks and STEM activities.

• In Topic 2 STEM Project (8.EE.2.6), students use linear equations to explore demography, connecting linear equations to predictions of population growth. "Develop a linear equation to represent population growth after x years.”
• Topic 3 Performance Task, Form A (8.F.1 and 8.F.2): “Sofia and Hector are captains of their track and field teams. As captains, they help their teammates train for the different events.” The following questions provide different information in graph and table form and five different questions about this scenario.

The instructional materials for enVision Florida Mathematics Grade 8 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

All three aspects of rigor are present in program materials. With few exceptions, lessons are connected to two aspects of rigor with an emphasis on application. Student practice includes all three aspects of rigor, though there are fewer questions for conceptual understanding.

There are instances where all three aspects of rigor are present independently throughout the program materials.

• Lesson 4-1: Students develop conceptual understanding about constructing scatter plots to interpret the relationship of paired data.
• Lesson 2-3: Students develop procedural skills using the distributive property to solve multi-step equations.
• Lesson 1-10: Students apply scientific notation using operations: “The total consumption of fruit juice in a particular country in 2006 was about 2.28 x $$10^9$$ gallons. The population of that country that year was 3 x $$10^8$$. What was the average number of gallons consumed per person in that country in 2006?”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

• In Lesson 7-2, students build conceptual understanding about using of the Converse of the Pythagorean Theorem to identify right angles. In Lesson 7-3, students use the Pythagorean Theorem and its converse in real-world problems like solving for the longest poster to fit in a given box and whether the angle of a ramp meets recommendations of horizontal distance for every foot of vertical rise.
• Throughout Topic 3, conceptual understanding about functions is developed and applied using real-world problems. Lesson 3-1 Question 11: Students identify if a relation is a function. “Taylor has tracked the number of students in his grade since third grade. He records his data in the table below. Is the relation a function? Explain.” Lesson 3-3, Question 1: Students compare linear and nonlinear functions. “Justin opens a savings account with $4. He saves $2 each week. Does a linear function or a nonlinear function represent this situation? Explain.” Lesson 3-5, Question 2: Students investigate intervals of increase and decrease. “How would knowing the slope of a linear function help determine whether a function is increasing or decreasing?” Lesson 3-6, Question 9: Students sketch functions from verbal descriptions: “Melody starts at her house and rides her bike for 10 minutes to a friend’s house. She stays at her friend’s house for 60 minutes. Sketch a graph that represents this description.”

For some standards that emphasize conceptual understanding, the materials do not provide students a consistent opportunity to develop understanding of the mathematical content within the standard and quickly transition to developing procedural skills around the mathematical content. An example of this includes:

• Lesson 7-1 Understand the Pythagorean Theorem has an emphasis on conceptual understanding and procedural fluency: “Students learn and understand the Pythagorean Theorem.” The lesson starts with: “Kelly drew a right triangle on graph paper. Kelly says that the sum of the areas of squares with side lengths a and b is the same as the area of the square with side length c. Do you agree with Kelly? Explain.” Example 1 shows pictures that develop the proof of the theorem and includes $$a^2+b^2=c^2$$. Example 2 immediately moves into Use the Pythagorean Theorem. The rest of the lesson and practice uses procedural steps.

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

All eight MPs are clearly identified throughout the materials in numerous places, including:

• The Program Overview book begins by listing the eight Topics and their connections to standards and practices.
• The Table of Contents in the Program Overview book connects every lesson to standards and practices.
• The Math Practice and Problem Solving Handbook includes a list of the Mathematical Practice Standards and real-world scenarios modeled through questions and answers.  
• The online tools offer a video, “Math Practices Animation,” for each MP, with explanations of the Math Practices as well as problems that demonstrate the practice.  
• Topic Overviews contain bulleted descriptions of how MPs are addressed and what mathematically proficient students should do.
• Topic Planner Tables at the beginning of each Topic in the TE connect standards and practices to descriptions of each lesson.
• Lesson Overviews include indications of Math Practices within a lesson. For example, in Lesson 6-2, states, “MP.2.1 Reason Abstractly and Quantitatively: Students will analyze the relationship between random samples and populations to make inferences about populations. They will compare different samples from the same populations.”
• In Student Practice problems, MPs are labeled with descriptions within problems. For example, Lesson 7-3 Do you Understand, question 2 says, “Look for Structure: How is using the Pythagorean Theorem in a rectangular prism similar to using it in a rectangle?”

The MPs are consistently used to enrich the mathematical content. For example:

• MP.7.1 enriches the mathematical content when students justify that a relationship is proportional when represented as a graph and then flexibly use graphs to describe proportional relationships. Lesson 2-6 identifies MP7.1 as an emphasis for students to analyze and solve Linear Equations. Do You Understand? For example, Question 3 “Why is the slope between any two points on a straight line always the same?” Practice and Problem Solving Question 9 says, “The points (2.1, -4.2) and (2.5, -5) form a proportional relationship. What is the slope of the line that passes through these two points?”
• MP.2.1 enriches the mathematical content as students expand their knowledge about rational numbers and the relationships with decimals and fractions when explaining their answer. Lesson 1-1, Question 16: ”When writing a repeating decimal as a fraction, why does the fraction always have only 9s or 9s and 0s as digits in the denominator?”
• MP.8.1 enriches the mathematical content when students recognize the mistake as using a + b = c instead of $$a^2+b^2=c^2$$, demonstrating that they’ve practiced using the equation $$a^2+b^2=c^2$$ and see the patterns of the equation in similar situations. Lesson 7-2, Question 13: “Three students draw triangles with the side lengths shown. All three say their triangle is a right triangle. Which students are incorrect? Which mistake might they have made?”

Because the Mathematical Practices are labeled in so many places, they are not always consistent and are often overidentified. The identification is broad, rather than targeted, with labels being most relevant at the lesson level. For example:

• In Lesson 1-5, the Table of Contents lists MPs 2.1, 3.1, 4.1, 7.1, & 8.1, but MPs 2.1 and 7.1 are listed in the Lesson Overview. MP.2.1 and 7.1 are integrated into the lesson; however, the other MPs are not a major part of the lesson.
• All 3-Act Math lessons identify all eight MPs, and the questions within 3-Act Math lessons are identical in each topic.
• Multiple MPs are identified for every lesson.

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet the expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Student materials consistently prompt students to both construct viable arguments and analyze the arguments of others.

• Lesson 3-4, Practice and Problem Solving, Construct Arguments: “Suppose another store sells a similar package, modeled by a linear function with initial value $7.99. Which store has the better deal? Explain.”
• Lesson 1-2, Explain It!: “Sofia wrote a decimal as a fraction. Her classmate Nora says that her method and answer are not correct. Sofia disagrees and says that this is the method she learned (graphic shown). Is Nora or Sofia correct?”
• Lesson 3-1, Practice and Problem Solving, Question 10: “During a chemistry experiment, Sam records how the temperature changes over time using ordered pairs (time in minutes, temperature in ℃). Is the relation a function? Explain.”
• Lesson 3-6, Explain It!: “The Environmental Club is learning about oil consumption and energy conservation around the world. Jack says oil consumption in the United States has dropped a lot. Ashley says oil consumption in China is the biggest problem facing the world environment. A) Do you agree or disagree with Jack’s statement? Construct an argument based on the graph to support your position. B) Do you agree or disagree with Ashley’s statement? Construct an argument based on the graph to support your position.”
• Lesson 1-2, Practice and Problem Solving, Question 13: “Deena says that 9.565565556… is a rational number because it has a repeating pattern. Do you agree? Explain.”
• Lesson 2-1, Practice and Problem Solving, Question 14 page 109: “Your friend solved the equation 4x + 12x - 6 = 4(4x + 7) and got x = 34. What error did your friend make? What is the correct solution?”
• Lesson 4-2, Practice and Problem Solving, question 3 page 220: “How does the scatter plot of a nonlinear association differ from that of a linear association?”

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet the expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking.

• Solve & Discuss It! or Explain It! at the beginning of each lesson include guidance for teachers to Facilitate Meaningful Mathematical Discourse. In Lesson 6-7 Solve and Discuss It!, the materials prompt teachers to “Ask students to share their solutions. If needed, project Melanie’s and Nick’s work and ask: 'How does Nick’s observation differ from Melanie’s? Do you think Melanie’s Answer or Nick’s answer is more complete? Explain.'”
• In the Visual Learning portion of the lesson, there are sections labeled, Elicit and Use Evidence of Student Thinking and Convince Me. In Lesson 8-4, the materials prompt teachers with, “A cone and a sphere have the same radius and height. Which will make the cone have the same volume as the sphere, doubling the radius of the cone or doubling the height of the cone? Explain.”
• The 3-Act Mathematical Modeling activities prompt teachers to ask students about their predictions. “Ask about predictions. Why do you think your prediction is the answer to the Main Question? Who had a similar prediction? How many of you agree with that prediction? Who has a different prediction?”
• When MP.3.1 is identified as the emphasis of the lesson, teachers are provided with question prompts in the Lesson Overview and “look fors” such as: “How can you justify your answer? What mathematical language, models, or examples will help you support your answer? How could you improve this argument? How could you use counterexamples to disprove this argument? What do you think about this explanation? What question would you ask about the reasoning used?” In Lesson 1-1, the materials prompt teachers with, “As students work through the Explain It, listen and look for different ways in which students analyze Sofia’s work. Incorporate their critiques into the classroom discussion.”

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet the expectations that materials use accurate mathematical terminology.

The materials use precise and accurate mathematical terminology and definitions, and support students in using them. Teacher editions, student books, and all supplemental materials explicitly attend to the specialized language of mathematics.

• Each Topic Overview lists the vocabulary being introduced for each lesson. In Topic 2 Analyze and Solve Linear Equations, the vocabulary listed for the lessons includes: slope, y-intercept, and slope-intercept form.  
• New vocabulary terms are highlighted in the text and definitions are provided within the sentence where each term is found. In Lesson 2-8,  the term y-intercept is highlighted, and the definition is provided within the sentence. “The y-coordinate of the point where the line crosses the y-axis is the y-intercept.”
• A Glossary in the back of Volume 1 lists all the vocabulary terms.
• A Vocabulary Review is included in the Topic Review. Students are provided with explicit vocabulary practice. In Topic 4 Review, page 247, Use Vocabulary in Writing: “Describe the scatter plot at the right. Use vocabulary terms in your description.”

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that there is a clear distinction between problems and exercises in the materials.

There are eight Topics in each grade level. Each Topic presents lessons in a consistent structure. During the instructional sections, which include guided instruction, step-by step procedures, and problem solving, students work on examples and problems to learn new concepts.

At the end of the lesson, a variety of exercises allow students to independently show their understanding of the material. The exercises also include Higher Order Thinking, a Lesson Quiz, and Additional Practice.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that the design of assignments is intentional and not haphazard.

Lessons follow a consistent format that sequences assignments intentionally.

• In Solve and Discuss It, students are introduced to concepts and procedures through a problem-based situation.
• Visual Learning: This portion of instruction connects to the problem learned previously and is the substance of the lesson. There are three different examples explored to create student understanding.
• Do You Understand? These exercises generally promote conceptual understanding from the lesson.
• Do you Know How? These exercises generally promote procedural skill and fluency from the lesson.
• Practice and Problem Solving: These are a mix of rigorous exercises and include application problems.

Lessons are in a logical order that build coherence throughout the grade level. Exercises are intentional to encourage a progression of understanding and skills.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that the instructional materials prompt students to show their mathematical thinking in a variety of ways. For example:

• Lesson 3-1: Students identify functions using arrow diagrams and ordered pairs.
• Lesson 1-6: Students use a table or the Quotient of Powers Property to explain expressions with negative and zero exponents.
• Lesson 7-2: Students construct arguments and justify their reasoning concerning the Converse of the Pythagorean Theorem.
• Lesson 1-2: Students construct an argument and justify reasoning about another student’s response to a number being rational or not.
• Lesson 2-2: Students build a model for a problem by using diagrams and equations.
• Lesson 3-2: Students use a diagram and a coordinate plane to represent a linear equation.

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of virtual manipulatives, but the materials do not include physical manipulatives.

• Manipulatives and other mathematical representations are consistently aligned to the mathematical content in the standards, and virtual manipulatives are used for developing conceptual understanding, such as bar diagrams or geometric objects.
• The materials have manipulatives embedded within Visual Learning Animation Plus for many lessons and also within Independent Practice and Differentiated Intervention activities.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide teachers with quality questions for students.

In the Teacher Edition, facilitator notes for each activity include questions for the teacher to guide students' mathematical development and to elicit students' understanding. The materials indicate that questions provided are intended to provoke thinking and provide facilitation through the mathematical practices as well as getting the students to think through their work. For example:

• Lesson 1-4: “Of all the possible floor dimensions, which floor dimension has the greatest perimeter? The least?”
• Lesson 2-8: “If you created a graph with Alex’s age on the x-axis, what number might you count by? Explain.”
• Lesson 3-6: “How many intervals does the sketch show? Explain.”
• Topic 7, STEM: “What criteria might you consider when designing your slanted roof system to collect rainwater?”
  

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide teachers guidance for presenting the content and using embedded technology for student learning.

• The Topic Overview includes Math Background for the Topic. This provides a big picture of the learning throughout the lessons. The Math Background also looks at how Focus, Coherence, and Rigor, as well as the Mathematical Practices, are addressed within the Topic.
• Each STEM Activity provides teachers with background information on the math, science, and engineering and technology found in the activity. In addition, it gives information on how to present the topic, including discussion questions. It also gives direction on when to show the STEM video, and when the project can be launched.

In each lesson teachers are provided with the following guidance:

• Information about how to activate prior knowledge is given in the Review What You Know! section. A Vocabulary Review activity is also given, as well as instructions on preparing students for reading success.
• A Lesson Overview that includes the Objectives, Essential Understandings, descriptions of how the mathematical content builds over the grades and within the topic, and how rigor is addressed in the lesson. In addition, both the content and the practice standards addressed in the lesson are described.
• Tips on what to do before, during, and after problems are available for the teacher.
• Technology enhancement included in the online program is noted in the teacher materials, though specific games/lessons/videos/online tools must be accessed online for teachers to know what they include.  
  

The instructional materials for enVision Florida Mathematics Grade 8 explain the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Each topic opens with a Topic Overview that includes a Math Background for the Topic.
• The Coherence section has three parts: Look Back, Topic ____, and Look Ahead. Each section gives a clear, specific explanation of how the topic is connected across grades.
• Each topic includes a Review What You Know! section. The section includes a practice page for students, questions for teachers to activate prior student knowledge, and a vocabulary review.
• Teacher Edition Program Overview Materials contain an overview of mathematics for K-12.
  

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

The Assessment Sourcebook and the Teacher Program Overview provide information about the use of assessments to gather information about students' prior knowledge. Every grade level includes a Grade Level Readiness test. The Topic Readiness Assessment in each Topic helps teachers gather information about students’ prior knowledge within and across grade levels. Topic Readiness assessments can also be taken online, where they are auto-scored, and interventions are auto-assigned.

There is a Review What You Know assignment at the beginning of each Topic that helps students activate prior knowledge and prepare for the skills needed in the Topic. Each of these assignments has questioning strategies for the teacher. Each lesson also provides information for the teacher about prior and current grade levels and future math that is used.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

• Lesson 3-6, Error Intervention Item 12: “If students confuse the input and output, review how to label the axes correctly.”
• Lesson 1-2, Prevent Misconceptions Item 5: “Students may have trouble identifying 2,500 as a perfect square. Look at the first two digits in 2,500. Is 25 a perfect square? What is its square root? 2,500 is equal to 25 times 100. Is 100 a perfect square? What is the square root of 100?”
  

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• Each Topic includes a “Review what you know/Concept and Skills Review” section that includes a Vocabulary review and Practice problems. This section includes review and practice on concepts that are related to the new Topic.
• The Cumulative/Benchmark Assessments found at the end of Topics 2, 4, 6 and 8 provide review of prior topics as an assessment. An Item Analysis is provided for diagnosis and intervention. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores.
• The Math Diagnosis and Intervention System has practice pages which are specific to a skill or strategy (i.e. Markups and Markdowns and Mental Math).
• There are multiple pages of extra practice available at Pearson Realize online that give students extra opportunities to review skills assigned by the teacher. Each of these pages is able to be customized by the teacher or used as is.
• Different games online at Pearson Realize support students in practice and review of skills, as well procedural fluency.
• Teacher materials in print and online complement each other in many instances; however, It is worth noting that teachers who only use the print materials will miss the extensive resources available online, as the print edition has some notes that point teachers to the digital materials, but does not identify the full extent of the online resources. Digital assessments are auto-scored (page viii) and generate reports that can help with grouping and differentiation (page xii)Each Topic includes a Review what you know/Concept and Skills Review section that includes a Vocabulary review and Practice problems. This section includes review and practice on concepts that are related to the new Topic.
• The Cumulative/Benchmark Assessments found at the end of Topics 2, 4, 6, and 8 provide review of prior topics as an assessment. An Item Analysis is provided for diagnosis and intervention. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores.
• The Math Diagnosis and Intervention System has practice pages which are specific to a skill or strategy (i.e., Markups and Markdowns and Mental Math).
• There are multiple pages of extra practice available at Pearson Realize online that give students extra opportunities to review skills assigned by the teacher. Each of these pages is able to be customized by the teacher or used as is.
• Different games online at Pearson Realize support students in practice and review of skills, as well procedural fluency.

Teacher materials in print and online complement each other in many instances; however, It is worth noting that teachers who only use the print materials will miss the extensive resources available online, as the print edition has some notes that point teachers to the digital materials but does not identify the full extent of the online resources. Digital assessments are auto-scored, page viii, and generate reports that can help with grouping and differentiation, page xii.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that assessments clearly denote which standards are being emphasized.

The Item Analysis for Diagnosis and Remediation clearly denotes which standards are being assessed. This is found for all of the assessments, including the quizzes.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The Topic Overview in the Teacher Edition includes a section on Coherence which enhances the opportunity to scaffold instruction by identifying prerequisite skills that students should have.

All lessons include instructional notes and classroom strategies that provide teachers with sample questions, differentiation strategies, discussion questions, possible misconceptions, and what to look for from students, which provides structure for the teacher in making content accessible to all learners. Often, the Practice & Problem Solving section begins with scaffolded problems for students. In the Solve and Discuss It! section, teachers are given questions for before, during, and after the activity that provide scaffolding for students. For example:

• Topic 8, Lesson 8-1: Before: “What everyday objects are cylinders?” During: "When you take the top off a can what is its shape? If you break apart the rest of a can and flatten it out, what are the rest of the shapes?” After: "Is Ky correct when he writes that the longest side of the rectangle is equal to the circumference of the circle?”
  

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

• There are Response to Intervention strategies in each lesson. These sections give teachers “look fors” and suggestions to address the needs of students who are struggling. Questions for the teacher to ask are also included.
• Each lesson has at least one Additional Example. These help students cement or extend their understanding of the concept being taught. It includes an extra problem for the teacher to use, as well as questions to help elicit meaningful responses.
• Each lesson has Differentiated Interventions for a wide-range of learners:
• Reteach to Build Understanding provides scaffolding to reteach.
• Additional Vocabulary Support helps students with key vocabulary.
• Build Mathematical Literacy provides support for struggling readers.
• Enrichment extends concepts from the lesson.
• Online Math Tools and Games build understanding and fluency.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials embed tasks with multiple entry-points.

Lessons begin with Problem-Based Learning, including Solve & Discuss It or Explore It, and can often be solved with a variety of solution strategies. Also, 3-Act Mathematical Modeling and Performance Tasks include questions with multiple entry points that can be solved using a variety of representations.

• Explore It! “Calvin and Mike do sit-ups when they work out. They start with 64 sit-ups for the first set and do half as many each subsequent set.  A) What representation can you use to show the relationship between the set number and the number of sit-ups? B) What conclusion can you make about the relationship between the number of sit-ups in each set?” Sample answers show two entry points to answering part B.

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials suggest support, accommodations, and modifications for English Language Learners and other special populations.

• Each lesson has support, accommodations and modifications for ELL students.
• During lessons, strategies are given for teachers to address different levels of English Language Learners such as:
• Emerging: “Ask students to identify which parts of the illustration show ‘four matches.’ Ask the students: 'What other meanings do you know for the word match? Explain. How can the illustration help you know which meaning to use?'”
• Expanding: “English Language Learners may not understand the questions asked. Have students state the problem in their own words.”

An English Language Learners Toolkit suggests teaching strategies, assessment tips, vocabulary and reading strategies, and discussion and problem-solving grouping ideas.

• Two pages of multilingual thinking words include the following languages: English, Spanish, Chinese, Vietnamese, Korean, and Hmong.
• There is also a limited list of key vocabulary in the same 6 languages.
• Teaching Math to Culturally and Linguistically Diverse Students provides tips and strategies.

Each chapter has Prepare for Reading Success that gives teachers pre-reading strategies to help all students access the language of the topic. For example, one strategy is Making Predictions, where there are teacher questioning strategies, as well as work for students that involves making predictions regarding the content. It also includes an extension for all readers.

Another special population that is addressed is Early Finishers. Each lesson addresses these students' needs by asking an additional question for students to ponder that correlates with the essential question in the lesson. 

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Each lesson offers differentiated instruction to extend the concepts in the lesson and provides opportunities to challenge advanced students. For example:

• Lesson 5-1 Enrichment Example 1: “Challenge students to complete the table showing the characteristics and number of solutions for different possibilities of two lines.”
• Lesson 5-1 Challenge Item 15: “Challenge students to change this system of equations so it has a different solution.”

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide a balanced portrayal of various demographic and personal characteristics.

For example:

• Different cultural names and situations are represented in the materials, ie., Sandra, Nadia, Nigel, Yoshi, Joaquin, Archie.
• The materials avoid pronouns, referencing a role instead, ie., the carpenter, the teacher, a plumber, the cross country team.
• There are few pictures of actual people in the Student Book, mostly objects or cartoonish drawings.